Q.Obtain the simplest logical expression of the following and draw the corresponding switching circuit: $[p \vee (\sim q \vee \sim r)] \wedge (p \vee (q \wedge r))$

The (reconstructed) expression is $[p \vee (\sim q \vee \sim r)] \wedge [p \vee (q \wedge r)]$.

This has the form $(p \vee X) \wedge (p \vee Y)$ with $X = \sim q \vee \sim r$ and $Y = q \wedge r$. By the distributive law, $(p \vee X) \wedge (p \vee Y) \equiv p \vee (X \wedge Y)$.

So the expression becomes $p \vee [(\sim q \vee \sim r) \wedge (q \wedge r)]$. …

Distributive law to factor $p$, then complement law collapses the …

Not verifying the reconstructed bracket against a truth table before simplifying a garbled source expression, or dropping the identity/complement …